Michigan Mathematical Journal
- Michigan Math. J.
- Volume 69, Issue 1 (2020), 41-78.
Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field
Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semidistance , which he introduced for analytic spaces defined over a non-Archimedean metrized field . We prove various characterizations of smooth projective varieties for which is an actual distance.
Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve defined over . We prove a non-Archimedean analogue of the equivalence between having a negative Euler characteristic and the normality of certain families of analytic maps taking values in .
Michigan Math. J., Volume 69, Issue 1 (2020), 41-78.
Received: 3 January 2018
Revised: 29 August 2018
First available in Project Euclid: 21 November 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
Secondary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Rodríguez Vázquez, R. Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field. Michigan Math. J. 69 (2020), no. 1, 41--78. doi:10.1307/mmj/1574326880. https://projecteuclid.org/euclid.mmj/1574326880